Need help selecting nozzles for sidewalk lawn strips

I recently bought a house with an existing lawn sprinkler system (Toro). On either side of my driveway, I have strips of grass between the sidewalk and the street. The east strip measures 7.5' by 25' and the west strip measures 7.5' by 16'.

I have dead brown spots in each of these strips that the sprinklers are not hitting. It appears to me that the existing nozzles are shooting over these spots and they aren't getting any water, while the areas farther from the sprinkler heads are green.

I really, really don't want to dig up the existing system to move or install additional heads. I am considering replacing the existing heads and nozzles with Rainbird 8ft HE-VAN and U-series dual spray nozzles. Supposedly they give more even coverage throughout the range of throw? The problem I see is that the 8ft thrown won't give me head-to-head coverage. What do you guys think?

The below drawings are of the two strips of grass, with the arcs showing the throw distance of the 8ft nozzles.

You're never going to cover that correctly the way the heads are spaced out.
If you don't mind watering the street go with the 15U's throughout. 8ft and I guarantee you'll make the brown spots bigger.
Where I live we have a sprinkler Nazi patrolling the streets giving people tickets for watering the street. I'm not joking. This guy gets 68k a year to look for people watering on the wrong day or whatever he can find. I should gone for that job. He picks his hours. Sometimes 3 am.

Sorry, but no one manufactures nozzles for your situation. Proper coverage requires different head locations, and probably lots more heads, were you to be in one of those wasting-water-gets-you-fined localities.

One of my problems is one the "East Strip" is on the same zone as my front yard, and the "West Strip" is on the same zone as half of my backyard. So I already have a bunch of other nozzles on these zones. I'm not sure how much water I have available, I tried doing a bucket test on an outside faucet but I believe it gave me a false low for my gpm because I just have small PEX plumbing going to that faucet.

For the larger "East Strip", do you think I should move heads to each of the four corners, then put a 12ft half spray at the midpoint of the 26' side and a 10ft half spray at the midpoint of the 21' side? Would that be better than what I have now? Then on the "West Strip" add 8ft half sprays to the midpoints there as well?